Finite Group Databasebeta

← C3×#10595468 #13175065

Subgroups — C3×#10595468 #13175065

Order 1728.

1356 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#41×C3⋊D3C211yesmaximal, characteristic
2C2×C3×#3797C211yesmaximal, characteristic, complemented
3C32×#951C212yesmaximal, complemented
4C3×#63945C212yesmaximal, complemented
5C3×#63944C212yesmaximal, complemented
6C3×#63931C212yesmaximal, complemented
7C3×#63930C212yesmaximal, complemented
8C3×#63833C212yesmaximal, complemented
9C3×#63818C211yesmaximal, characteristic, complemented
10C3×D3×#137—32nomaximal
11#10595468C311yesmaximal, characteristic, direct product factor
12C33×#41C2211yescharacteristic
13C3×#3832C2211yescharacteristic
14C3×Q8×C3⋊D3C2211yescharacteristic
15C3×#3830—21no—
16C3×#3830C2211yescharacteristic
17C3×D4×C3⋊D3—21no—
18C3×D4×C3⋊D3C2211yescharacteristic
19C3×#3828—21no—
20C3×#3828C2211yescharacteristic
21C2×C3×C4×C3⋊D3—21no—
22C2×C3×C4×C3⋊D3C2211yescharacteristic
23C2×C32×Dic6C2212yescomplemented
24C2×C3×#627—21no—
25C2×C3×#624—21no—
26C3×#3797—21no—
27C3×#3797—21no—
28C3×#3797C2212yes—
29C3×#3797C2212yescomplemented
30C32×#216C2214yescomplemented
31C32×#214C2214yescomplemented
32C32×#208C2212yescomplemented
33C3×#3719C2214yescomplemented
34C3×#3717C2214yescomplemented
35C3×#3712C2212yescomplemented
36C3×#3710C2212yes—
37#41×C3⋊D3C2×C311yescharacteristic
38C3×D3×#41—32no—
39C3×D3×#41—61no—
40C2×C3×D3×Q8—32no—
41C2×#3797C2×C311yescharacteristic, complemented
42C32×#137—32no—
43C3×#951—22no—
44C3×#951D312yescomplemented
45C3×#951C2×C312yescomplemented
46C3×#942—32no—
47C3×#918—34no—
48C3×D3×Q16—34no—
49C3×#915—34no—
50C3×D3×SD16—34no—
51C3×#909—32no—
52C3×D3×M16—32no—
53#63945C2×C312yescomplemented
54#63944C2×C312yescomplemented
55#63931C2×C312yescomplemented
56#63930C2×C312yescomplemented
57#63833C2×C312yescomplemented
58#63818C2×C311yescharacteristic, complemented
59C22×C3×C3⋊D3—21no—
60C22×C3×C3⋊D3D411yescharacteristic
61C33×Q8C2311yescharacteristic
62C33×D4—21no—
63C33×D4C2311yescharacteristic
64C2×C33×C4—21no—
65C2×C33×C4C2311yescharacteristic
66C3×#638—21no—
67C3×#638—21no—
68C3×#638—21no—
69C2×C3×C3⋊Dic3—21no—
70C2×C3×C3⋊Dic3D411yescharacteristic
71C3×C4⋊(C3⋊D3)—21no—
72C3×C4⋊(C3⋊D3)C2311yescharacteristic
73C3×C4×C3⋊D3—21no—
74C3×C4×C3⋊D3—21no—
75C3×C4×C3⋊D3—21no—
76C3×C4×C3⋊D3D411yescharacteristic
77C3×C4×C3⋊D3D411yescharacteristic
78C3×C4×C3⋊D3C2311yescharacteristic
79C3×C4×C3⋊D3C2311yescharacteristic
80C3×#634—21no—
81C3×#634C2311yescharacteristic
82C2×C32×Dic3—22no—
83C32×Dic6—22no—
84C32×Dic6C2314yes—
85C3×#627—22no—
86C3×#627—22no—
87C3×#624—22no—
88C3×#624—22no—
89C32×C3⋊C8C2314yes—
90C2×C3×#137—91no—
91D3×#137—32no—
92C32×#41—21no—
93C32×#41—22no—
94C32×#41—41no—
95C32×#41C2×D312yes—
96C32×#41C22×C311yescharacteristic
97C2×C32×Q8—32no—
98#3832C22×C311yescharacteristic
99Q8×C3⋊D3C22×C311yescharacteristic
100#3830—21no—
101#3830C22×C311yescharacteristic
102D4×C3⋊D3—21no—
103D4×C3⋊D3C22×C311yescharacteristic
104#3828—21no—
105#3828C22×C311yescharacteristic
106C2×C4×C3⋊D3—21no—
107C2×C4×C3⋊D3C22×C311yescharacteristic
108C3×#239—32no—
109C3×#239—61no—
110C3×D3×Q8—32no—
111C3×D3×Q8—34no—
112C3×D3×Q8—34no—
113C3×D3×Q8—62no—
114C3×D3×Q8—62no—
115C3×D3×Q8—61no—
116C3×#237—32no—
117C3×#237—62no—
118C3×#237—61no—
119C3×#237—62no—
120C3×D3×D4—32no—
121C3×D3×D4—62no—
122C3×D3×D4—61no—
123C3×D3×D4—62no—
124C3×#235—32no—
125C3×#235—62no—
126C3×#235—61no—
127C3×#235—62no—
128C2×C3×C4×D3—32no—
129C2×C3×C4×D3—62no—
130C2×C3×C4×D3—62no—
131C2×C3×C4×D3—61no—
132C2×C3×C4×D3—62no—
133C2×C3×Dic6—22no—
134C2×C3×Dic6—62no—
135C2×C3×Dic6C2×D312yescomplemented
136C2×C3×Dic6C22×C312yescomplemented
137C2×#627—21no—
138C2×#624—21no—
139#3797—21no—
140#3797—21no—
141#3797C22×C312yes—
142#3797C22×C312yescomplemented
143C32×Q16—34no—
144C32×SD16—34no—
145C32×M16—32no—
146C3×#216—24no—
147C3×#216—34no—
148C3×#216C2×D314yescomplemented
149C3×#216C22×C314yescomplemented
150C3×#215—34no—
151C3×#214—24no—
152C3×#214C2×D314yescomplemented
153C3×#214C22×C314yescomplemented
154C3×#208—22no—
155C3×#208C2×D312yescomplemented
156C3×#208C22×C312yescomplemented
157C3×Dic12—34no—
158C3×#204—34no—
159C3×ΓL(1,𝔽25)—34no—
160C3×D3×C8—34no—
161#3719C22×C314yescomplemented
162#3717C22×C314yescomplemented
163#3712C22×C312yescomplemented
164#3710C22×C312yes—
165C22×C33—21no—
166C22×C33C2×D411yescharacteristic
167C2×C3×C3⋊D3—22no—
168C2×C3×C3⋊D3—21no—
169C2×C3×C3⋊D3—42no—
170C2×C3×C3⋊D3C2×D411yescharacteristic
171C2×C3×C3⋊D3C2×D411yescharacteristic
172C33×C4—21no—
173C33×C4C2×D411yescharacteristic
174C33×C4C2411yescharacteristic
175C3×C3⋊Dic3—21no—
176C3×C3⋊Dic3C2×D411yescharacteristic
177C3×C3⋊Dic3C2×D411yescharacteristic
178C32×Dic3—24no—
179C2×C3×#41—91no—
180C22×C3×Q8—91no—
181D3×#41—32no—
182D3×#41—61no—
183C2×D3×Q8—32no—
184C3×#137—32no—
185C3×#137—32no—
186C3×#137—62no—
187C3×#137—92no—
188C3×#137—92no—
189C3×#137—92no—
190C2×C3×Q16—92no—
191C2×C3×SD16—92no—
192C2×C3×M16—91no—
193#951C3×D312yescomplemented
194#942—32no—
195#918—34no—
196D3×Q16—34no—
197#915—34no—
198D3×SD16—34no—
199#909—32no—
200D3×M16—32no—
201C22×C3⋊D3—21no—
202C22×C3⋊D3C3×D411yescharacteristic
203C22×C3×D3—32no—
204C22×C3×D3—61no—
205C22×C3×D3—62no—
206C22×C3×D3—62no—
207C32×Q8—21no—
208C32×Q8—22no—
209C32×Q8—34no—
210C32×Q8—41no—
211C32×Q8—62no—
212C32×Q8C22×D312yes—
213C32×Q8C23×C311yescharacteristic
214C32×D4—21no—
215C32×D4—22no—
216C32×D4—22no—
217C32×D4—21no—
218C32×D4—22no—
219C32×D4—41no—
220C32×D4—42no—
221C32×D4—42no—
222C32×D4C22×D312yes—
223C32×D4C23×C311yescharacteristic
224C2×C32×C4—21no—
225C2×C32×C4—22no—
226C2×C32×C4—22no—
227C2×C32×C4—21no—
228C2×C32×C4—22no—
229C2×C32×C4—41no—
230C2×C32×C4—42no—
231C2×C32×C4—42no—
232C2×C32×C4—62no—
233C2×C32×C4C22×D312yes—
234C2×C32×C4C23×C311yescharacteristic
235#638—21no—
236#638—21no—
237#638—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3C3×D411yescharacteristic
240C4⋊(C3⋊D3)—21no—
241C4⋊(C3⋊D3)C23×C311yescharacteristic
242C4×C3⋊D3—21no—
243C4×C3⋊D3—21no—
244C4×C3⋊D3—21no—
245C4×C3⋊D3C3×D411yescharacteristic
246C4×C3⋊D3C3×D411yescharacteristic
247C4×C3⋊D3C23×C311yescharacteristic
248C4×C3⋊D3C23×C311yescharacteristic
249#634—21no—
250#634C23×C311yescharacteristic
251C3×#67—62no—
252C3×#67—62no—
253C3×#67—62no—
254C3×#67—62no—
255C3×#67—62no—
256C3×#67—62no—
257C2×C3×Dic3—22no—
258C2×C3×Dic3—22no—
259C2×C3×Dic3—32no—
260C2×C3×Dic3—42no—
261C2×C3×Dic3—61no—
262C2×C3×Dic3—62no—
263C2×C3×Dic3—62no—
264C3×D12—32no—
265C3×D12—61no—
266C3×D12—62no—
267C3×D12—62no—
268C3×C4×D3—32no—
269C3×C4×D3—32no—
270C3×C4×D3—32no—
271C3×C4×D3—32no—
272C3×C4×D3—61no—
273C3×C4×D3—61no—
274C3×C4×D3—61no—
275C3×C4×D3—61no—
276C3×C4×D3—64no—
277C3×C4×D3—64no—
278C3×C4×D3—62no—
279C3×C4×D3—62no—
280C3×C4×D3—62no—
281C3×C4×D3—62no—
282C3×C4×D3—62no—
283C3×C4×D3—62no—
284C3×Dic6—22no—
285C3×Dic6—22no—
286C3×Dic6—24no—
287C3×Dic6—32no—
288C3×Dic6—42no—
289C3×Dic6—61no—
290C3×Dic6—64no—
291C3×Dic6—64no—
292C3×Dic6—62no—
293C3×Dic6—62no—
294C3×Dic6C22×D314yes—
295C3×Dic6C23×C314yes—
296#627—22no—
297#627—22no—
298#624—22no—
299#624—22no—
300C32×C8—34no—
301C3×C3⋊C8—24no—
302C3×C3⋊C8C22×D314yes—
303C3×C3⋊C8C23×C314yes—
304C2×#137—91noSylow
305C2×C33—21no—
306C2×C33—41no—
307C2×C33C22×D411yescharacteristic
308C3×C3⋊D3—21no—
309C3×C3⋊D3—41no—
310C3×C3⋊D3#13712yescomplemented
311C3×#41—21no—
312C3×#41—22no—
313C3×#41—41no—
314C3×#41—91no—
315C3×#41—91no—
316C3×#41—91no—
317C3×#41—181no—
318C3×#41—181no—
319C3×#41D3211yescharacteristic
320C3×#41C2×C3×D312yes—
321C2×C3×Q8—32no—
322C2×C3×Q8—32no—
323C2×C3×Q8—62no—
324C2×C3×Q8—92no—
325C2×C3×Q8—92no—
326C2×C3×Q8—91no—
327C2×C3×Q8—181no—
328C2×C3×Q8—181no—
329C2×C3×Q8—181no—
330C2×C3×D4—91no—
331C2×C3×D4—181no—
332C22×C3×C4—91no—
333C22×C3×C4—181no—
334C22×C3×C4—181no—
335#239—32no—
336#239—61no—
337D3×Q8—32no—
338D3×Q8—34no—
339D3×Q8—34no—
340D3×Q8—61no—
341D3×Q8—62no—
342D3×Q8—62no—
343#237—32no—
344#237—61no—
345#237—62no—
346#237—62no—
347D3×D4—32no—
348D3×D4—61no—
349D3×D4—62no—
350D3×D4—62no—
351#235—32no—
352#235—61no—
353#235—62no—
354#235—62no—
355C2×C4×D3—32no—
356C2×C4×D3—61no—
357C2×C4×D3—62no—
358C2×C4×D3—62no—
359C2×C4×D3—62no—
360C2×Dic6—62no—
361C2×Dic6C2×C3×D312yescomplemented
362C3×Q16—34no—
363C3×Q16—34no—
364C3×Q16—64no—
365C3×Q16—94no—
366C3×SD16—34no—
367C3×SD16—34no—
368C3×SD16—64no—
369C3×SD16—94no—
370C3×M16—32no—
371C3×M16—32no—
372C3×M16—62no—
373C3×M16—92no—
374C2×C3×C8—92no—
375#216—34no—
376#216C2×C3×D314yescomplemented
377#215—34no—
378#214C2×C3×D314yescomplemented
379#208C2×C3×D312yescomplemented
380Dic12—34no—
381#204—34no—
382ΓL(1,𝔽25)—34no—
383D3×C8—34no—
384C22×C32—21no—
385C22×C32—22no—
386C22×C32—22no—
387C22×C32—21no—
388C22×C32—22no—
389C22×C32—41no—
390C22×C32—42no—
391C22×C32—42no—
392C22×C32D3×D412yes—
393C22×C32C2×C3×D411yescharacteristic
394C2×C3⋊D3—21no—
395C2×C3⋊D3—22no—
396C2×C3⋊D3—42no—
397C2×C3⋊D3C2×C3×D411yescharacteristic
398C2×C3⋊D3C2×C3×D411yescharacteristic
399C2×C3×D3—32no—
400C2×C3×D3—32no—
401C2×C3×D3—61no—
402C2×C3×D3—61no—
403C2×C3×D3—64no—
404C2×C3×D3—62no—
405C2×C3×D3—62no—
406C2×C3×D3—122no—
407C2×C3×D3—124no—
408C2×C3×D3—124no—
409C32×C4—21no—
410C32×C4—22no—
411C32×C4—22no—
412C32×C4—21no—
413C32×C4—22no—
414C32×C4—21no—
415C32×C4—22no—
416C32×C4—41no—
417C32×C4—41no—
418C32×C4—42no—
419C32×C4—42no—
420C32×C4—64no—
421C32×C4D3×D412yes—
422C32×C4C2×C3×D411yescharacteristic
423C32×C4C23×D312yes—
424C32×C4C24×C311yescharacteristic
425C3⋊Dic3—21no—
426C3⋊Dic3C2×C3×D411yescharacteristic
427C3⋊Dic3C2×C3×D411yescharacteristic
428C3×Dic3—24no—
429C3×Dic3—24no—
430C3×Dic3—32no—
431C3×Dic3—32no—
432C3×Dic3—44no—
433C3×Dic3—61no—
434C3×Dic3—61no—
435C3×Dic3—62no—
436C3×Dic3—62no—
437C2×#41—91no—
438C22×Q8—91no—
439#137—32no—
440#137—92no—
441#137—92no—
442#137—92no—
443C2×Q16—92no—
444C2×SD16—92no—
445C2×M16—91no—
446C33C2×#13711yescharacteristic, complemented, Sylow
447C23×C3—91no—
448C23×C3—181no—
449C22×D3—32no—
450C22×D3—61no—
451C22×D3—62no—
452C22×D3—62no—
453C3×Q8—21no—
454C3×Q8—22no—
455C3×Q8—34no—
456C3×Q8—34no—
457C3×Q8—41no—
458C3×Q8—64no—
459C3×Q8—62no—
460C3×Q8—62no—
461C3×Q8—91no—
462C3×Q8—122no—
463C3×Q8—181no—
464C3×Q8—182no—
465C3×Q8—182no—
466C3×Q8C2×D3211yescharacteristic
467C3×Q8C22×C3×D312yes—
468C3×D4—22no—
469C3×D4—21no—
470C3×D4—22no—
471C3×D4—21no—
472C3×D4—22no—
473C3×D4—42no—
474C3×D4—42no—
475C3×D4—41no—
476C3×D4—91no—
477C3×D4—181no—
478C3×D4—181no—
479C3×D4—181no—
480C3×D4—181no—
481C3×D4C2×D3211yescharacteristic
482C3×D4C22×C3×D312yes—
483C2×C3×C4—22no—
484C2×C3×C4—21no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—21no—
488C2×C3×C4—42no—
489C2×C3×C4—42no—
490C2×C3×C4—41no—
491C2×C3×C4—62no—
492C2×C3×C4—62no—
493C2×C3×C4—91no—
494C2×C3×C4—91no—
495C2×C3×C4—91no—
496C2×C3×C4—91no—
497C2×C3×C4—91no—
498C2×C3×C4—122no—
499C2×C3×C4—181no—
500C2×C3×C4—181no—
501C2×C3×C4—182no—
502C2×C3×C4—182no—
503C2×C3×C4—181no—
504C2×C3×C4—181no—
505C2×C3×C4C2×D3211yescharacteristic
506C2×C3×C4C22×C3×D312yes—
507#67—62no—
508#67—62no—
509#67—62no—
510#67—62no—
511#67—62no—
512#67—62no—
513C2×Dic3—22no—
514C2×Dic3—32no—
515C2×Dic3—61no—
516C2×Dic3—62no—
517C2×Dic3—62no—
518D12—32no—
519D12—61no—
520D12—62no—
521D12—62no—
522C4×D3—32no—
523C4×D3—32no—
524C4×D3—32no—
525C4×D3—32no—
526C4×D3—61no—
527C4×D3—61no—
528C4×D3—61no—
529C4×D3—61no—
530C4×D3—64no—
531C4×D3—64no—
532C4×D3—62no—
533C4×D3—62no—
534C4×D3—62no—
535C4×D3—62no—
536C4×D3—62no—
537C4×D3—62no—
538Dic6—22no—
539Dic6—32no—
540Dic6—61no—
541Dic6—64no—
542Dic6—64no—
543Dic6—62no—
544Dic6—62no—
545Dic6C22×C3×D314yes—
546C3×C8—34no—
547C3×C8—34no—
548C3×C8—64no—
549C3⋊C8C22×C3×D314yes—
550C2×C32—21no—
551C2×C32—22no—
552C2×C32—21no—
553C2×C32—22no—
554C2×C32—41no—
555C2×C32—41no—
556C2×C32—42no—
557C2×C32—41no—
558C2×C32—42no—
559C2×C32—42no—
560C2×C32—81no—
561C2×C32—82no—
562C2×C32—82no—
563C2×C32C2×D3×D412yes—
564C2×C32C22×C3×D411yescharacteristic
565C3⋊D3—21no—
566C3⋊D3—41no—
567C3⋊D3C3×#13712yescomplemented
568C3×D3—34no—
569C3×D3—62no—
570C3×D3—62no—
571C3×D3—121no—
572C3×D3—122no—
573C3×D3—122no—
574#41—91no—
575#41—91no—
576#41—91no—
577#41—181no—
578#41—181no—
579#41C3×D3211yescharacteristic
580C2×Q8—32no—
581C2×Q8—92no—
582C2×Q8—92no—
583C2×Q8—91no—
584C2×Q8—181no—
585C2×Q8—181no—
586C2×Q8—181no—
587C2×D4—91no—
588C2×D4—181no—
589C22×C4—91no—
590C22×C4—181no—
591C22×C4—181no—
592Q16—34no—
593Q16—94no—
594SD16—34no—
595SD16—94no—
596M16—32no—
597M16—92no—
598C2×C8—92no—
599C22×C3—22no—
600C22×C3—21no—
601C22×C3—22no—
602C22×C3—21no—
603C22×C3—22no—
604C22×C3—42no—
605C22×C3—42no—
606C22×C3—41no—
607C22×C3—91no—
608C22×C3—91no—
609C22×C3—182no—
610C22×C3—181no—
611C22×C3—362no—
612C22×C3#381111yescharacteristic
613C22×C3C3×D3×D412yes—
614C2×D3—32no—
615C2×D3—32no—
616C2×D3—61no—
617C2×D3—61no—
618C2×D3—64no—
619C2×D3—62no—
620C2×D3—62no—
621C2×D3—122no—
622C2×D3—124no—
623C2×D3—124no—
624C3×C4—22no—
625C3×C4—21no—
626C3×C4—22no—
627C3×C4—22no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—22no—
631C3×C4—42no—
632C3×C4—42no—
633C3×C4—41no—
634C3×C4—41no—
635C3×C4—64no—
636C3×C4—64no—
637C3×C4—91no—
638C3×C4—91no—
639C3×C4—124no—
640C3×C4—181no—
641C3×C4#381111yescharacteristic
642C3×C4C3×D3×D412yes—
643C3×C4C22×D3211yescharacteristic
644C3×C4C23×C3×D312yes—
645Dic3—24no—
646Dic3—32no—
647Dic3—32no—
648Dic3—61no—
649Dic3—61no—
650Dic3—62no—
651Dic3—62no—
652C32—22no—
653C32—21no—
654C32—41no—
655C32D3×#13712yescomplemented
656C32C2×C3×#13711yescharacteristic, complemented
657C23—91no—
658C23—181no—
659Q8—34no—
660Q8—62no—
661Q8—91no—
662Q8—181no—
663Q8—182no—
664Q8—182no—
665Q8C2×C3×D3211yescharacteristic
666D4—21no—
667D4—91no—
668D4—181no—
669D4—181no—
670D4—181no—
671D4—181no—
672D4C2×C3×D3211yescharacteristic
673C2×C4—21no—
674C2×C4—62no—
675C2×C4—91no—
676C2×C4—91no—
677C2×C4—91no—
678C2×C4—91no—
679C2×C4—91no—
680C2×C4—181no—
681C2×C4—181no—
682C2×C4—182no—
683C2×C4—182no—
684C2×C4—181no—
685C2×C4—181no—
686C2×C4C2×C3×D3211yescharacteristic
687C8—34no—
688C2×C3—22no—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—22no—
692C2×C3—41no—
693C2×C3—42no—
694C2×C3—42no—
695C2×C3—42no—
696C2×C3—41no—
697C2×C3—41no—
698C2×C3—81no—
699C2×C3—82no—
700C2×C3—82no—
701C2×C3—92no—
702C2×C3—181no—
703C2×C3—361no—
704C2×C3C2×#381111yescharacteristic
705C2×C3C2×C3×D3×D412yes—
706D3—34no—
707D3—62no—
708D3—62no—
709D3—121no—
710D3—122no—
711D3—122no—
712C22—21no—
713C22—91no—
714C22—91no—
715C22—182no—
716C22—181no—
717C22—362no—
718C22C3×#381111yescharacteristic
719C4—21no—
720C4—64no—
721C4—91no—
722C4—91no—
723C4—181no—
724C4C3×#381111yescharacteristic
725C4C22×C3×D3211yescharacteristic
726C3—21no—
727C3—22no—
728C3—41no—
729C3#1059546811yescharacteristic, direct product factor
730C3C3×D3×#13712yescomplemented
731C2—21no—
732C2—41no—
733C2—92no—
734C2—181no—
735C2—361no—
736C2C2×C3×#381111yescharacteristic
subgroupG/H
centerC2×C3C2×#3811
commutator, cosocleC32×C4C24×C3
FrattiniC4C22×C3×D32
FittingC33×#41C22
socleC2×C33C22×D4
prime radicalC3×#41×C3⋊D3C2
hypercenterC3×#41D32
hypocenterC32C2×C3×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#41

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C3×#3797C2semidirect
3. C32×#951C2semidirect
4. C3×#63945C2semidirect
5. C3×#63944C2semidirect
6. C3×#63931C2semidirect
7. C3×#63930C2semidirect
8. C3×#63833C2semidirect
9. C3×#63818C2semidirect
11. #10595468C3direct (N × H)
23. C2×C32×Dic6C22semidirect
29. C3×#3797C22semidirect
30. C32×#216C22semidirect
31. C32×#214C22semidirect
32. C32×#208C22semidirect
33. C3×#3719C22semidirect
34. C3×#3717C22semidirect
35. C3×#3712C22semidirect
41. C2×#3797C2×C3semidirect
44. C3×#951D3semidirect
45. C3×#951C2×C3semidirect
53. #63945C2×C3semidirect
54. #63944C2×C3semidirect
55. #63931C2×C3semidirect
56. #63930C2×C3semidirect
57. #63833C2×C3semidirect
58. #63818C2×C3semidirect
135. C2×C3×Dic6C2×D3semidirect
136. C2×C3×Dic6C22×C3semidirect
142. #3797C22×C3semidirect
148. C3×#216C2×D3semidirect
149. C3×#216C22×C3semidirect
152. C3×#214C2×D3semidirect
153. C3×#214C22×C3semidirect
155. C3×#208C2×D3semidirect
156. C3×#208C22×C3semidirect
161. #3719C22×C3semidirect
162. #3717C22×C3semidirect
163. #3712C22×C3semidirect
193. #951C3×D3semidirect
310. C3×C3⋊D3#137semidirect
361. C2×Dic6C2×C3×D3semidirect
376. #216C2×C3×D3semidirect
378. #214C2×C3×D3semidirect
379. #208C2×C3×D3semidirect
446. C33C2×#137semidirect
567. C3⋊D3C3×#137semidirect
655. C32D3×#137semidirect
656. C32C2×C3×#137semidirect
729. C3#10595468direct (N × H)
730. C3C3×D3×#137semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#41×C3⋊D32
C2×C3×#37972
C32×#9512
C3×#639452
C3×#639442
C3×#639312
C3×#639302
C3×#638332
C3×#638182
C3×D3×#1373
#105954683